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1: Customize DLMF

…You can customize the appearance and functionality of the DLMF site using these selections. …

2: How to Cite

… ►Citations from other electronic media (the web, email, …), should, of course, use the appropriate means to give the site URL (https://dlmf.nist.gov/), or specific Permalinks. … ►For convenience, the permalink can be found in the pop-up ‘Info box’ associated with each item in the site.

3: Bibliography K

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

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1st item.

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Dark optical solitons: Physics and applications. Physics Reports 298 (2-3), pp. 81–197.

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External Links:

Document

Referenced by:

§22.19(iii).

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Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)]. J. Chem. Phys. 121 (2), pp. 1167.

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External Links:

Document

Referenced by:

§8.24(ii).

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A Program for Computing the Conical Functions of the First Kind $P_{-1/2+i\tau }^m(x)$ for $m=0$ and $m=1$ . Comput. Phys. Comm. 23 (1), pp. 51–61.

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Notes:

Single-precision Fortran, maximum accuracy 15D.

External Links:

Document, Code

Referenced by:

§14.31(ii), 1st item.

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Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).

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External Links:

ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

Referenced by:

§22.19(iv).

Encodings:

BibTeX

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4: About MathML

… ►MathML (Mathematical Markup Language), is an open, international standard, to represent the mathematical content on the web and elsewhere. … ►Most modern browsers support ‘Web Fonts’, fonts that are effectively included with a web site. DLMF uses the STIX web font to provide a consistent coverage. …

5: 6 Exponential, Logarithmic, Sine, and
Cosine Integrals

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6: 7 Error Functions, Dawson’s and Fresnel Integrals

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7: DLMF Project News

error generating summary

8: Bibliography T

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Une nouvelle représentation explicite des nombres d’Euler. C. R. Acad. Sci. Paris Sér. A-B 286 (19), pp. A807–A809.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§24.6.

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Rational Chebyshev approximation for the Fermi-Dirac integral $F_{-3/2}(x)$ . Solid–State Electronics 41 (5), pp. 771–773.

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Document

Referenced by:

§25.21(vii).

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Further comments on the computation of modified Bessel function ratios. Math. Comp. 35 (151), pp. 937–939.

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External Links:

ISSN 0025-5718, FullText, Document, MathReview (James M. Horner), ZentralBlatt

Referenced by:

§10.74(v).

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Sul comportamento asintotico dell’$n$-esimo polinomio di Laguerre nell’intorno dell’ascissa $4n$ . Comment. Math. Helv. 22, pp. 150–167.

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External Links:

ISSN 0010-2571, Document, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§18.16(iv).

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9: 27 Functions of Number Theory

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10: 7.24 Approximations

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Cody (1968) gives minimax rational approximations for the Fresnel integrals (maximum relative precision 19S); for a Fortran algorithm and comments see Snyder (1993).

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Luke (1969b, pp. 323–324) covers $\frac{1}{2}\sqrt{\pi }\mathrm{erf}x$ and ${\mathrm{e}}^{x^2}F\left(x\right)$ for $-3\le x\le 3$ (the Chebyshev coefficients are given to 20D); $\sqrt{\pi }x{\mathrm{e}}^{x^2}\mathrm{erfc}x$ and $2xF\left(x\right)$ for $x\ge 3$ (the Chebyshev coefficients are given to 20D and 15D, respectively). Coefficients for the Fresnel integrals are given on pp. 328–330 (20D).

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